※ 引述《PttFund (批踢踢基金)》之銘言：
: Suppose that f in R([a,b]). Show that f^2 in R([a,b]).
: Notation: R([a,b]) is the set of all Riemann integrable
: functions on [a,b].
Since f belongs to R([a,b])
f is bounded, i.e. |f| < M for some M > 0
and for any ε > 0
there is a partition Π on [a,b] such that
U(f;Π) - L(f;Π) < ε/2M
consider U(f^2;Π) - L(f^2;Π) < 2M [U(f;Π) - L(f^2;Π)] < ε
by Darboux's Criterion
f^2 belongs to R([a,b])
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 218.160.37.84